Anyway, back to the OP.
There’s no reason for the Qataris to be happy to see us in the sense that they were desperate for military protection in these times or anything. Aside from some border disputes and skirmishes with Saudi Arabia and Bahrain, Qatar hasn’t really been threatened by anyone since independence.
However, they could be said to be happy to see us the way someone is happy to see an old friend stop by. The US and Qatar have been allies for a long while, with the US and the UK the first to recognize Qatar’s independence and helped pave the way for them to join the UN as quickly as possible. Not only that, the Qataris are making a very admirable push towards a more open, liberal and democratic nation with their first parliamentary elections coming up in a year or two and new protections for press and speech freedom under their new sheikh. They may see US forces there as protection against groups who may see this is a threat and/or betrayal. The US and Qataris have a number of joint economic, diplomatic and educational projects going on, as well.
Plus, there have been accusations that certain members of the Qatari royal family have been harboring and supporting terrorists, so the government may see welcoming an American military presence as a way of helping to counteract those accusations.